Geodesic
Local characteristics of smoothing properties of endomorphisms of finite Abelian groups
Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 33-45 
V. O. Drelikhov; I. A. Kruglov. Local characteristics of smoothing properties of endomorphisms of finite Abelian groups. Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 3, pp. 33-45. http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a2/
@article{MVK_2015_6_3_a2,
     author = {V. O. Drelikhov and I. A. Kruglov},
     title = {Local characteristics of smoothing properties of endomorphisms of finite {Abelian} groups},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {33--45},
     year = {2015},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a2/}
}
TY  - JOUR
AU  - V. O. Drelikhov
AU  - I. A. Kruglov
TI  - Local characteristics of smoothing properties of endomorphisms of finite Abelian groups
JO  - Matematičeskie voprosy kriptografii
PY  - 2015
SP  - 33
EP  - 45
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a2/
LA  - ru
ID  - MVK_2015_6_3_a2
ER  - 
%0 Journal Article
%A V. O. Drelikhov
%A I. A. Kruglov
%T Local characteristics of smoothing properties of endomorphisms of finite Abelian groups
%J Matematičeskie voprosy kriptografii
%D 2015
%P 33-45
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/MVK_2015_6_3_a2/
%G ru
%F MVK_2015_6_3_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a finite Abelian group, $G^n$ be its $n$-fold Cartesian product, and $\vec\xi=(\xi_1,\xi_2,\dots,\xi_n)$ be a random element of $G^n$. We investigate the local characteristics of closeness of distribution of random element $H(\vec\xi\,)$, where $H\colon G^n\to G^m$, to the uniform distribution on $G^m$. Main results are connected with the case of independent identically distributed elements $\xi_1,\xi_2,\dots,\xi_n$ and endomorphism $H$ of group $G^n$ onto the group $G^m$.

[1] Egorov B. A., Maksimov Yu. I., “Ob odnoi posledovatelnosti sluchainykh velichin, prinimayuschikh znacheniya iz kompaktnoi kommutativnoi gruppy”, Teoriya veroyatn. i ee primen., 13:4 (1968), 621–630 | MR | Zbl

[2] Kapitonov V. M., “O skorosti skhodimosti posledovatelnosti raspredelenii, opredelyaemykh skhemoi avtoregressii na kompaktnoi gruppe”, Teoriya veroyatn. i ee primen., 18:3 (1973), 608–615 | MR | Zbl

[3] Maksimov Yu. I., “O tsepyakh Markova, svyazannykh s dvoichnymi registrami sdviga so sluchainymi elementami”, Trudy po diskretnoi matematike, 1, 1997, 203–220 | MR | Zbl

[4] Chung F., Diaconis P., Gracham R. L., “A random walk problem arising in random number generation”, Ann. Probab., 15:3 (1987), 1148–1165 | DOI | MR | Zbl

[5] Hildebrand M., “Random processes of the form $X_{n+1}=a_n\cdot X_n+b_n(\operatorname{mod}\,p)$”, Ann. Probab., 21:2 (1993), 710–720 | DOI | MR | Zbl

[6] Grenander U., Veroyatnosti na algebraicheskikh strukturakh, Mir, M., 1965, 274 pp. | MR

[7] Solodovnikov Vik. I., “Bent-funktsii iz konechnoi abelevoi gruppy v konechnuyu abelevu gruppu”, Diskretnaya matematika, 14:1 (2004), 99–113 | DOI | MR | Zbl